We propose a joint test to detect whether an Itô semimartingale exhibits drift and/or volatility explosions. The joint test exploits simultaneous estimation of the localized average of the increments and the localized return autocovariance to capture different explosion patterns as a function of the localizing window. Using infill asymptotics on irregularly sampled and noisy observations, we show that the test allows to pin down the location of the drift and volatility explosion rates. Simulations show the effectiveness of our methodology in small samples and allow to study the power and the size of our test. We provide an empirical application, where we detect drift and volatility explosions in high-frequency financial data contaminated by market microstructure noise.
This is a joint work with Roberto Renò (IDS Department, ESSEC Business School).
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